A new example of an algebraic surface with canonical map of degree 16
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In this note, we construct a minimal surface of general type with geometric genus \( p_g =4 \), self-intersection of the canonical divisor \( K^2 = 32\), and irregularity \( q = 1 \) such that its canonical map is an Abelian cover of degree 16 of \(\mathbb P^1\times \mathbb P^1\).
KeywordsSurfaces of general type Canonical maps Abelian covers
Mathematics Subject Classification14J29
The author is deeply indebted to Margarida Mendes Lopes for all her help and thanks Carlos Rito for many interesting conversations and suggestions. Thanks are also due to the anonymous referee for his/her thorough reading of the paper and suggestions.
- 2.Barth, W.P., Hulek, K., Peters, C.A.M., Van de Ven, A.: Compact Complex Surfaces, 2nd ed., vol. 4 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]. Springer, Berlin (2004)Google Scholar
- 4.Beauville, A.: Complex Algebraic Surfaces, 2nd ed., vol. 34 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge. Translated from the 1978 French original by R. Barlow, with assistance from N. I. Shepherd-Barron and M. Reid (1996)Google Scholar
- 6.Gleissner, C., Pignatelli, R., Rito, C.: New surfaces with canonical map of high degree. ArXiv e-prints (2018)Google Scholar
- 9.Persson, U.: Double coverings and surfaces of general type. In: Algebraic Geometry (Proc. Sympos., Univ. Tromsø Tromsø, 1977), vol. 687 of Lecture Notes in Math. Springer, Berlin, 168–195 (1978)Google Scholar